number 6

Code: PU  
P=10 (k=4)
10b+a = 4b+a (mod  6)
Formulae:
Number N is divisible by 6 iff 4b+a is divisible by 6

Example:
Number N  =
Number N  = 98760 =
4(   9876  )+0 =
4(4(  987+6)+0 =
4(4(4( 98+7)+6)+0 =
4(4(4(4*9+8)+7)+6)+0 =
4(4(    2+7)+6)+0 =
4(      3+6)+0 = 0 (mod 6)
is divisible by 6.

Number N =
Number N  = 176 =
4( 17)+6 =
4(4*1+7)+6 =
4*  5+6 = 2 (mod 6) isn't divisible by 6.



Code: PU  
P=8 (k=2)
8b+a = 2b+a (mod  6)
Formulae:
Number N is divisible by 6 iff 2b+a is divisible by 6

Example:
Number N  = 754 =
2( 75)+4 =
2(2*7+5)+4 =
2*  1+4 = 0 (mod 6)
is divisible by 6.

Number N =
Number N  = 172 =
2( 17)+2 =
2(2*1+7)+2 =
2*  1+2 = 4 (mod 6) isn't divisible by 6.



Code: PD
P=4, (k=2)
4b+a = 6b-2b+a = -2b+a (mod 6)
Formulae:
Number N is divisible by 6 iff -2b+a is divisible by 6

Example:

Number N  = 322 =
-2(  32)+2 =
-2(-2*3+2)+2 =
-2*   2+4 = 0 (mod 6)
is divisible by 6.

Number N =
Number N  = 130 =
-2(  13)+0 =
-2(-2*1+3)+0 =
-2*   1+0 = -2 = 4 (mod 6) isn't divisible by 6.